Problem: What do the following two equations represent? $-x-3y = -1$ $9x-3y = 2$
Solution: Putting the first equation in $y = mx + b$ form gives: $-x-3y = -1$ $-3y = x-1$ $y = -\dfrac{1}{3}x + \dfrac{1}{3}$ Putting the second equation in $y = mx + b$ form gives: $9x-3y = 2$ $-3y = -9x+2$ $y = 3x - \dfrac{2}{3}$ The slopes are negative inverses of each other, so the lines are perpendicular.